290
Air Pollution and Turbulence: Modeling and Applications
11.2.2 EARLY INVERSION TECHNIQUES
The initial CO 2 inversion study (Bolin and Keeling, 1963) modeled atmospheric
transport as a one-dimensional diffusion process, by taking averages of over height
and longitude. Diffusive models have been used in studies of restricted domains
(Heimann and Keeling, 1986; Keeling and Heimann, 1986) and for analyzing illconditioning and error statistics (Newsam and Enting, 1988; Enting and Newsam,
1990; Enting, 1993). However, in most contexts, explicit consideration of the advective nature of atmospheric transport is essential. A class of low-resolution models,
used for inversion of halogenated gases, are the box models used in the AGAGE study
(and its predecessors) (Prinn et al., 2000). Early mass-balance inversions used twodimensional models (averaged over longitude). Most recent inversions, particularly
for CO 2 , have used full three-dimensional transport models.
Very early in the development of trace gas inversions, two main types of calculations emerged:
Mass-balance inversion: In this technique, an atmospheric transport model is run
with boundary conditions specifi ed in terms of concentrations, and surface fl uxes
are deduced from the requirement of local conservation of mass. The technique was
developed using two-dimensional models (Enting and Mansbridge, 1989; Tans et al.,
1989; Enting and Mansbridge, 1991; Conway et al., 1994), but there has been some
later work with 3-D models (Law, 1999) requiring extensive interpolation of concentration data. Dargaville and Simmonds (2000) developed a related “data-assimilation” technique, using multiple model runs to interpolate the concentration data.
Synthesis inversion: In this technique, defi ned by Equations 11.5a and b, the source
is broken into blocks with specifi ed space–time distributions of fl uxes multiplied by
unknown scale factors. For each block, concentrations resulting from unit sources
are calculated using a transport model. The fl uxes are estimated by the process of
estimating the scale factors. This was done by fi tting observed concentrations with
a linear combination of the calculated concentrations. Early applications (Keeling
et al., 1989; Tans et al., 1990) used ad hoc fi ts. The process was formalized as one of
(Bayesian) statistical estimation by Enting et al. (1993, 1995). The term “synthesis”
was apparently fi rst used for this type of inversion in the study of methane by Fung
et al. (1991).
The mass-balance technique takes the equations for a vector of concentrations c(t)
with elements c j (t) and transport T j (c(t)):
=
+
d ( )
( ( ))
( ) for all sites
dt
j
j
j
c t T t
S t
c
(11.5a)
and, for a set of surface sites, rewrites them as
=
−
d
( )
( )
( ( )) for surface sites
dt
j
j
j
S t
c t T t
c
(11.5b)
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
11.2.2 EARLY INVERSION TECHNIQUES
The initial CO 2 inversion study (Bolin and Keeling, 1963) modeled atmospheric
transport as a one-dimensional diffusion process, by taking averages of over height
and longitude. Diffusive models have been used in studies of restricted domains
(Heimann and Keeling, 1986; Keeling and Heimann, 1986) and for analyzing illconditioning and error statistics (Newsam and Enting, 1988; Enting and Newsam,
1990; Enting, 1993). However, in most contexts, explicit consideration of the advective nature of atmospheric transport is essential. A class of low-resolution models,
used for inversion of halogenated gases, are the box models used in the AGAGE study
(and its predecessors) (Prinn et al., 2000). Early mass-balance inversions used twodimensional models (averaged over longitude). Most recent inversions, particularly
for CO 2 , have used full three-dimensional transport models.
Very early in the development of trace gas inversions, two main types of calculations emerged:
Mass-balance inversion: In this technique, an atmospheric transport model is run
with boundary conditions specifi ed in terms of concentrations, and surface fl uxes
are deduced from the requirement of local conservation of mass. The technique was
developed using two-dimensional models (Enting and Mansbridge, 1989; Tans et al.,
1989; Enting and Mansbridge, 1991; Conway et al., 1994), but there has been some
later work with 3-D models (Law, 1999) requiring extensive interpolation of concentration data. Dargaville and Simmonds (2000) developed a related “data-assimilation” technique, using multiple model runs to interpolate the concentration data.
Synthesis inversion: In this technique, defi ned by Equations 11.5a and b, the source
is broken into blocks with specifi ed space–time distributions of fl uxes multiplied by
unknown scale factors. For each block, concentrations resulting from unit sources
are calculated using a transport model. The fl uxes are estimated by the process of
estimating the scale factors. This was done by fi tting observed concentrations with
a linear combination of the calculated concentrations. Early applications (Keeling
et al., 1989; Tans et al., 1990) used ad hoc fi ts. The process was formalized as one of
(Bayesian) statistical estimation by Enting et al. (1993, 1995). The term “synthesis”
was apparently fi rst used for this type of inversion in the study of methane by Fung
et al. (1991).
The mass-balance technique takes the equations for a vector of concentrations c(t)
with elements c j (t) and transport T j (c(t)):
=
+
d ( )
( ( ))
( ) for all sites
dt
j
j
j
c t T t
S t
c
(11.5a)
and, for a set of surface sites, rewrites them as
=
−
d
( )
( )
( ( )) for surface sites
dt
j
j
j
S t
c t T t
c
(11.5b)
© 2010 by Taylor and Francis Group, LLC